Are elevated moist layers a blind spot for hyperspectral infrared sounders?-A model study

The ability of the hyperspectral satellite based passive infrared (IR) instrument IASI to resolve Elevated Moist Layers (EMLs) within the free troposphere is investigated. EMLs are strong moisture anomalies with significant impact on the radiative heating rate profile and typically coupled to freezing level detrainment from convective cells in the tropics. A previous case study by Stevens et al. (2017) indicated inherent deficiencies of passive satellite based remote sensing instruments to resolve an EML. In this work, we first put the findings of Stevens et al. (2017) into the context of other retrieval case studies of EML5 like structures, showing that such structures can in principle be retrieved, but retrievability depends on the retrieval method and the exact retrieval setup. To approach a first more systematic analysis of EML retrievability, we introduce our own basic Optimal Estimation (OEM) retrieval, which for the purpose of this study is based on forward modelled (synthetic) clear-sky observations. By applying the OEM retrieval to the same EML case as Stevens et al. (2017) we find that a lack of independent temperature information can significantly deteriorate the humidity retrieval due to a strong temperature inversion at the EML 10 top. However, we show that by employing a wider spectral range of the hyperspectral IR observation, this issue can be avoided and EMLs can generally be resolved. We introduce a new framework for the identification and characterisation of moisture anomalies, a subset of which are EMLs, to specifically quantify the retrieval’s ability of capturing moisture anomalies. The new framework is applied to 1288 synthetic retrievals of tropical ocean short-range forecast model atmospheres, allowing for a direct statistical comparison of moisture anomalies between the retrieval and the reference dataset. With our basic OEM retrieval, we 15 find that retrieved moisture anomalies are on average 17 % weaker and 15 % thicker than their true counterparts. We attribute this to the retrieval smoothing error and the fact that rather weak and narrow moisture anomalies are most frequently missed by the retrieval. Smoothing is found to also constrain the magnitude of local heating rate extremes associated with moisture anomalies, particularly for the strongest anomalies that are found in the lower to mid troposphere. In total, about 80 % of moisture anomalies in the reference dataset are found by the retrieval. Below 5 km altitude, this fraction is only on the order of 20 52 %. We conclude that the retrieval of lower to mid tropospheric moisture anomalies, in particular of EMLs, is possible when the anomaly is sufficiently strong and its thickness is at least on the order of about 1.5 km. This study sets the methodological basis to more comprehensively investigate EMLs based on real hyperspectral IR observations and their operational products in the future.

conducted an observational case study of an EML present during the NARVAL-2 (Next Generation Remote Sensing for Validation Studies) measurement campaign. One method they deployed was a satellite retrieval analysis based on passive microwave and infrared ::::::::::: hyperspectral ::::::: infrared :::: (IR) : observations, both of which showed very poor performance in capturing the EML structure, suggesting that EMLs present a somewhat fundamental blind spot for passive satellite observations. This study aims at more comprehensively investigating the question whether EMLs really present a blind spot and where the limitations in resolving such moisture structures are, based on the IASI (Infrared Atmospheric Sounding Interferometer) instrument. We start out with the hypothesis that due to the EMLs association with particularly stratified layers, a good representation of the vertical temperature structure is key for resolving the moisture structure .

The retrieval
Extracting atmospheric state variables such as the temperature or concentrations of atmospheric constituents from passive satellite observations generally poses an inversion problem. The forward problem of calculating spectral radiances for a given atmospheric state in the clear sky case can be solved by a radiative transfer model (also "forward model") because the physical concepts of clear sky radiative transfer are well understood and quantified. However, due to the ill-posedness of the inverse problem and the non-linear nature of the forward model, a retrieval requires sophisticated methods to regularise the problem and find an optimal solution.
The spectral signal of water vapor depends not only on the atmospheric water vapor itself but also on the temperature.

Retrieval quantities
The quantities targeted for retrieval in this study are the profiles of water vapor volume mixing ratio (VMR H2O ), temperature (T ) and the surface temperature (T s ). They are represented by the retrieval state vector x: The water vapor profile is retrieved in natural logarithmic units, which is favourable for two reasons. On the one hand ::::: Firstly, 210 VMR H2O is a quantity that ranges over several orders of magnitude from a few percent near the surface to O(10 −6 ) in the upper troposphere and above, which is numerically inconvenient for the optimisation algorithm. On the other hand ::::::: Secondly, the transformation to logarithmic units avoids the possibility of physically implausible negative VMR values.
The one variable not explained up to now is γ, which is a non-dimensional positive integer that allows the LM scheme to be a weighted version of both a Gauss-Newton scheme (γ = 0) and a gradient descent scheme (γ = ∞). In our implementation, γ = 10 is arbitrarily chosen as a starting value and is adjusted to assure a reduction of the cost function with every iteration .

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This is particularly advantageous for cases where the starting point is far away from the solution, in which the Gauss-Newton scheme may struggle to converge. This makes the LM scheme in general more robust than the Gauss-Newton scheme. The tradeoff is that for cases where the starting point is rather close to the solution the LM scheme typically converges slower than the Gauss-Newton scheme.

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The radiative transfer model used in this study is version 2.3.1279 :::: 2.5.0 of the Atmospheric Radiative Transfer Simulator (ARTS). A comprehensive and compact description of ARTS is provided by Eriksson et al. (2011) and Buehler et al. (2018) and more documentation can be found on the ARTS website (https://www.radiativetransfer.org). Here, only the features that are directly relevant for the conducted retrieval calculations are presented.
For a body of a given temperature and emissivity ARTS calculates the emitted radiation and its transmission through a given Gaussian noise with a standard deviation of 0.2 :: 0.1 K for wavenumbers below 1750 cm −1 and 0.3 K above 1750 cm −1 is added to the forward simulated spectra : to :::::::: represent ::: the :::::::::: radiometric ::::: noise :: of ::::: IASI ::::: within ::: the ::::::: spectral ::::: range :::: used :: in :::: this ::::: study ). The sensor is assumed to be in 850 km altitude and to have a nadir viewing direction. The atmospheric 260 cases simulated are limited to clear-sky and are above ocean surfaces, where the surface emissivity in the spectral region covered by IASI is assumed to be 1.
The ARTS internal OEM module, which is part of the latest release ::::: ARTS ::: as :: of version 2.4.0of ARTS, is used to conduct the actual retrieval calculations.

A priori assumptions 265
The a priori assumptions about the atmospheric state are defined as the knowledge about the state prior to the measurement.
Although the true state is always known within the frame of this model study, the a priori knowledge is chosen based on information that would also be available in the situation of a real measurement. The a priori knowledge is represented by an a priori state vector x a and a covariance matrix S a . For the definition of the a priori state the tropical mean atmospheric state from the profile database of Anderson et al. (1986) is used as a basis, which from now on will be referred to as tropical FASCOD Where not stated otherwise, the a priori surface temperature is assumed to be the true surface temperature with an added Gaussian noise of 1.5 K. The Gaussian noise aims to simulate the accuracy of a real a priori surface temperature estimate, which can for example be obtained from AVHRR (Advanced Very High Resolution Radiometer), which together with IASI is part of the MetOp satellites :::::::: satellite's payload. Here, 1.5 K is a very conservative assumption for tropical ocean surfaces since uncertainties in AVHRR sea surface temperature data records are typically an order of magnitude lower, e.g. estimated at 0.18 K in the dataset of Merchant et al. (2019).
The a priori temperature profile is assumed to be moist adiabatic up to around 100 hPa. The a priori surface temperature is used as a starting point for the moist adiabat. A moist adiabatic tropospheric temperature profile is a reasonable assumption because the temperature lapse rate is mostly set to be moist adiabatic within the tropics by deep convection and by the 280 homogenisation of the temperature field by gravity waves due to the lack of a Coriolis force (Sobel and Bretherton, 2000).
Around 100 hPa and above, the moist adiabat is relaxed to the tropical FASCOD atmosphere with a hyperbolic tangent weighting function to represent the tropopause and the atmosphere above. The a priori VMR H2O profile is defined by combining a fixed relative humidity profile (RH) and the a priori temperature profile by using the relation: The fixed tropical FASCOD RH profile is used and the equilibrium pressure of water vapor e s (T ) is calculated based on the a priori temperature profile. p is the atmospheric pressure in a given altitude. e s (T ) ::::: e s (T ) : is calculated as the equilibrium pressure over water for temperatures above the triple point and over ice for temperatures more than 23 K below the triple point. For intermediate temperatures the equilibrium pressure is computed as a combination of the values over water and ice according to the IFS documentation (ECMWF, 2018).

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The a priori assumption about the variability of the retrieval quantities is encoded by S a , which consists of blocks for each retrieval quantity. For the surface temperature, a variance of 100 K 2 is assumed. The diagonal elements of the temperature profile block of S a (Fig. 2b) are calculated based on tropical ocean profiles from the database provided by Eresmaa and McNally (2014), which is based on the ECMWF IFS forecast model with a focus on a broad sampling of temperature profiles.
The nondiagonal elements are calculated based on a correlation length that linearly increases from 2.5 km at the surface to 295 10 km at and above the tropopause.
For the water vapor covariances (Fig. 2c), the approach of Schneider and Hase (2011) is adapted, where the diagonal elements of the log-scale water vapor covariances are set to 1 in the troposphere and linearly reduce to 0.25 within the stratosphere. An adjustment made here is that below 2 km, which is a crude estimate for the boundary layer height above ocean surfaces, the diagonal value linearly decreases to 0.1 at the surface. This better represents the generally fixed moisture structure near the 300 tropical ocean surface. The nondiagonal elements are calculated based on the same correlation length approach as for the temperature covariances.
An additional constraint about the atmospheric variability is introduced by filling in values for the cross-covariances between the three retrieval quantities. The diagonals of the cross covariance blocks are calculated as the product of the diagonals of the two respective covariance blocks, multiplied with a scale factor that exponentially decreases from 1 at the surface to 1/e in a 305 given altitude. This altitude is chosen to be 100 m for the cross covariance between surface temperature and temperature to represent the dependence of the atmospheric temperature on the surface temperature. Between temperature and water vapor the altitude is chosen to be 1000 m to represent the dependence of water vapor on temperature within the boundary layer, where the water vapor content is mainly constrained by the saturation pressure, which is mainly a function of temperature. The nondiagonal elements of the cross-covariances are calculated with the same correlation length approach as for temperature and , temperature (b) and the cross-covariance matrix between water vapor and temperature (a) used for the retrieval in this study. Each of these matrices constitutes a block within the full covariance block matrix Sa(introduced in Eq. ??. Note that it is sufficient to show only one cross-covariance matrix block, since Sa is block symmetric.
EMLs can be described as layers of anomalously large humidity, raising the question what one implicitly assumes the humidity to be increased against. Besides the actual humidity profile (be it in terms of VMR H2O ), one unconsciously also envisions a somewhat arbitrary climatological mean profile that smoothly decreases with height, against which the actual 320 humidity profile partly appears anomalously moist in the presence of an EML. This idea can be used to introduce a quantitative identification and characterisation method of moisture anomalies, a subset of which are EMLs.
At the core of this moisture anomaly identification method is the definition of a reference humidity profile, against which the anomalies occur. There are several ways a reference profile can be constructed and the suitability of a definition depends on the aim of the analysis. For example, a simple climatological mean profile may be a suited reference if one is interested 325 in the mean anomaly (e.g. the bias) of a test dataset of humidity profiles. However, for the purpose of this study it is not of interest whether a humidity profile is generally rather moist or dry, but instead only anomalous vertical variability of humidity is of interest. This is because the vertical moisture variability is what manifests as a footprint on the heating rate profile (Q) and thereby affect the vertical stability or even yield vertical motion (Albright et al., 2020).
To capture moisture anomalies closely related to the vertical moisture variability, the reference profile is constructed by 330 least-square fitting a quadratic function to the log(VMR H2O ) profile of the troposphere up to 100 hPa. A quadratic function is preferable over a linear function because in many cases the VMR H2O profile shows large scale non-exponential variability which should not interfere with the more small-scale anomalies we want to characterise. The following function is used as the reference water vapor profile: The humidity at the surface is represented by VMR H2O, ref (z = 0) = exp(c) and is fixed to the surface value of the actual humidity profile. The altitude z is used as a height coordinate for fitting because compared to pressure it has the benefit that z = 0 at the surface. The coefficients a and b are determined by least-square fitting to the logarithm of the humidity profile between the surface and 100 hPa because the assumed relation becomes less valid closer to the tropopause. After calculating the reference profile, moisture anomalies can be identified and characterised.
The atmospheric test case used here is constructed to be similar to the EML case investigated by Stevens et al. (2017). The testcase is constructed based on the tropical FASCOD atmosphere (Anderson et al., 1986). The VMR of water vapor and the temperature profiles of the tropical FASCOD atmosphere are modified to represent the typical structures associated with 345 an EML scenario. The EML associated structures include a distinct moisture inversion (increase of VMR H2O with height) with maximum humidity at around 650 hPaand a temperature inversion . ::::::::::: Temperature ::::::::: inversions : at the EML top . Another temperature inversion is located ::: and at the distinct drop of moisture at around 900 hPa , similar to the case investigated by Stevens et al. (2017) ::: are :::: also :::::: present :::: (not :::::: shown).
Figure 3(b) shows the close relation between the vertical humidity structure and the net heating rate Q (longwave + short-350 wave), which is calculated with the radiative transfer model RRTMG (Rapid Radiative Transfer Model for GCMs, Mlawer et al., 1997) through its implementation in the radiative convective equilibrium model konrad (Kluft and Dacie, 2020). Q is calculated for all conducted retrievals throughout this study to assess whether the vertical humidity structure is captured in a way in which also Q is represented well.

Reference dataset and retrieval error
The retrieval is applied to tropical ocean atmospheres (between 30°S to 30°N) that are part of the ECMWF IFS diverse profile database made available by Eresmaa and McNally (2014). The database consists of 25,000 short-range forecasts, which are divided into five even subsets that focus on representing diversity in a particular atmospheric quantity, such as temperature, 535 specific humidity or precipitation. For the purpose of this work, only the tropical ocean atmospheres of the subset that focuses on a diverse sampling of specific humidity is considered. This yields a total number of 1599 atmospheric setups, for 1438 :::: 1288 of which the retrieval converges to a solution. The following analysis is based on these converged cases.
A statistical overview of the variety :::::::: variability of temperature and humidity profiles covered by the tropical ocean dataset is provided in Fig. 6(a), (b) and (c). The temperature profiles show very limited variability, as is typical for tropical ocean 540 regions. However, despite this very smooth appearance of the vertical temperature structure, the individual profiles do include significant temperature inversions, for example the very prominent inversion in about 2 km height in the trade wind region (not shown). The humidity profiles show weak variability within the boundary layer, where the ocean acts as a humidity source and humidity is mostly set by the saturation vapor pressure controlled by temperature. The median RH is about 82 % at the surface and reaches its maximum in about 500 m height in the transition to the shallow cloud layer. In the free troposphere, the typical 545 "C" shape structure of the RH profile is followed (Romps, 2014). An interesting feature in the 75th and 90th percentiles of the RH profiles is the presence of positive RH anomalies in the layer between around 500 and 700 hPa, indicating moisture anomalies that may be tied to the freezing level. to 700 hPa the VMR H2O and RH biases are positive, while the temperature bias is slightly negative. This positive moisture bias in the lower troposphere is associated with an increased variability of the error, particularly towards strong positive errors that 555 indicate an overestimation of moisture in the lower troposphere by the retrieval. This may be caused by the typical hydrolapse that is coupled to the trade inversion in the trade wind regions, which can in its sharpness not be captured by the retrieval.
In the mid troposphere between about 700 to 300 hPa, which is where typical EMLs are expected, no significant temperature or humidity biases are found. A positive skewness in the VMR H2O error distribution towards strong positive errors is found, indicating that positive errors in retrieved VMR H2O are rare, but large compared to the negative errors that occur. As an 560 explanation for this error pattern, we propose the idea that positive (moist) moisture anomalies tend to be captured with a slight underestimation in their strength, while occasionally strong negative (dry) moisture anomalies beneath are associated with a strong overestimation of moisture by the retrieval due to a lack of signal beneath a positive moisture anomaly (as shown in Fig. 5). This could explain less frequent but strong positive retrieval errors and more frequent, but relatively weak negative errors that have a net bias close to zero.

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In the upper troposphere errors in temperature and humidity are generally larger. We believe that this has two causes. On the one hand the ::::: Firstly, ::: the : a priori moist adiabatic temperature assumption becomes worse closer to the tropopause. On the other hand ::::::: Secondly, Fig. 5 shows that there is only a weak radiative signal from the upper troposhere as indicated by strongly smoothed averaging kernels and a decreased vertical resolution. While this may be improved by adjusting the a priori assumptions for the upper troposphere and including even stronger absorption features of water vapor, the upper troposphere 570 is no major concern of this study.

Smoothing error
Part of the retrieval error shown in Fig. 6 can be attributed to the so called Smoothing Error (SE, Rodgers 2000). Given a specific observing system and a priori assumptions about the quantity to be observed, the SE is a source of error that can not be avoided without changing the observing system or a priori assumptions themselves. In the frame of the averaging kernel 575 matrix, the SE expresses the error in the retrieval that is associated with the non-delta-function shape of the averaging kernel rows (see Fig. 5) and the thereby limited ability to resolve vertical features. Here, it is calculated as where I n denotes the identity matrix of order n and n is the number of vertical levels of the profile retrieval. Figure 7 shows the SE statistics associated with the retrieved temperature and humidity profiles of the tropical ocean dataset.

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The median of the SE with respect to the temperature profile (SE(T ) ::::: SE(T )) is close to zero throughout most of the free troposphere, similar to the retrieval bias shown in Fig. 6(d). The positive retrieval bias in temperature found near the surface is with smaller magnitude also found in SE(T ) ::::: SE(T ), indicating that this pattern is caused by a systematically unresolved vertical feature. The variability of the temperature retrieval error found in Fig. 6(d) in the lower and mid troposphere cannot be attributed to smoothing, since the variability in SE(T ) is very small. In conclusion, this indicates that temperature error sources 585 are unlikely to be caused by uncaptured vertical temperature variability, but rather vertically constant biases ::::: errors, which do not show up in SE(T ). In the upper troposphere, SE(T ) increases towards the tropopause where smoothing becomes the major contribution to the retrieval temperature error.
For the water vapor profile in the lower and mid troposphere, smoothing is a greater source of error than for the temperature profile (Fig. 7b). While the median of the water vapor smoothing error (SE(log(VMR H2O ))) is low throughout the lower and 590 mid troposphere, its variability (e.g. the shown percentile ranges) is on similar scale as the variability of the retrieval error shown in Fig. 6(e). This indicates that a major contribution of error in the water vapor retrieval is to capture vertical variability.
The distribution of SE(log(VMR H2O )) in the mid troposphere also reflects the positive skewness that was found in the overall error in Fig. 6(e). This is consistent with the previously described idea that this skewness is linked to the retrieval's ability of capturing vertical moisture anomalies. In the upper troposphere, the median SE(log(VMR H2O )) increases to a similar 595 magnitude as the retrieval error, while its variability even exceeds that of the retrieval error, indicating that other sources of error are compensating.
The SE(RH) statistics show the combined effect of the smoothing errors in temperature and humidity (Fig. 7c). It is apparent that also in terms of RH the smoothing error has a strong contribution to the retrieval error in the lower and mid troposphere, similar to the VMR H2O error. In the upper troposphere the median SE(RH) ::::::: SE(RH) is on the same order as the retrieval error, 1288 tropical ocean atmospheres. Lines and shadings are defined as in Figure 6.

Retrieval of moisture anomalies
In this section the retrieval results for the previously introduced tropical ocean test dataset (Sect. 5) are assessed with specific focus on the characteristics of moisture anomalies as introduced in Sect. 3. First, the moisture anomaly characteristics of the tropical ocean dataset and of the retrieved dataset are compared to look for systematic limitations of the retrieval to resolve 605 specific kinds of moisture anomalies. Then, the impact of moisture anomalies on the heating rate profile is assessed and the retrieval's ability to capture this impact is investigated. distributions. The distributions of moisture anomaly height (z anom ) displayed in Fig. 8(a) show that most moisture anomalies occur in the mid to upper troposphere, which is somewhat surprising since EMLs are typically thought to be coupled to the freezing level in around 5 km height (Johnson et al., 1996;Stevens et al., 2017). However, note on the one hand ::::: firstly : that strong EMLs and very slight moisture anomalies are treated evenly here. On the other hand the :::::::: Secondly, ::: the : distributions reflect the statistics of the underlying dataset, which is based on the ECMWF IFS atmospheric model. This dataset appears as 615 a suitable starting point to assess the retrieval's ability to capture moisture anomalies, however, the analysis of the dataset's moisture anomaly statistics themselves are not the focus of this study. Figure 8(a) shows a bias between true and retrieved z anom of about 1.1 :: 0.9 km, which is caused by an :::::::: indicating :::: that ::: the :::::

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The distribution of the moisture anomaly strength (s anom ) depicted in Fig. 8(b) has a similar dynamical range as VMR H2O since the anomalous VMR H2O scales with its absolute value. The distribution of s anom of the retrieved dataset is overall shifted towards lower values yielding a negative bias of about −1.7 · 10 −4 (37 ::::::::: −8.2 · 10 −5 :::: (17 %) against the reference dataset, which can mostly be attributed to the smoothing error of the retrieval. The smoothing error generally acts by a weakening and thickening of anomalies, which also partly explains the significant positive bias of about 0.8 :: 0.4 km (28 :: 15 %) in moisture 640 anomaly thickness (∆ z anom ) depicted in Fig. 8(c). Another contributing effect towards the found biases in s anom and ∆ z anom is the fact that particularly weak and narrow moisture anomalies are more often completely missed by the retrieval as shown by Fig. 9.
6.2 Implications of moisture anomalies for the heating rate profile Moisture anomalies affect the heating rate profile by absorbing and emitting infrared :: IR : radiation. Because of the exponential 645 decrease of water vapor with height, emission at the anomaly top is particularly efficient and can yield a strong local radiative cooling rate (see Fig. 3). We consider this cooling effect to be the moisture anomaly's most prominent footprint on the heating rate profile. In the following, we quantify this cooling effect by considering the minimum heating rate within the vertical bounds of a moisture anomaly, min(Q anom ). Since min(Q anom ) is a scalar metric, it can intuitively be viewed as a function of moisture anomaly characteristics.  for the tropical ocean dataset and the retrieval dataset, respectively. Both datasets show a clear correlation between the two quantities, namely that stronger anomalies are associated with a stronger peak in radiative cooling. While moisture anomalies with s anom 10 −4 show similar minimum cooling rates down to about -2.5 K day −1 in both the reference and the retrieval dataset, larger differences between the two datasets are apparent for stronger anomalies. The reference dataset (Fig. 10, a)

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shows min(Q anom ) values between about -1 to -5 K day −1 for moisture anomalies with s anom 10 −4 , while the retrieval dataset barely shows any min(Q anom ) values smaller than -3 K day −1 .
We hypothesise that the increased variability in min(Q anom ) for s anom 10 −4 in the reference dataset can be attributed to the variability in the exact vertical shapes of the moisture anomalies. Anomalies with a strong negative moisture gradient at their top yield a stronger minimum in radiative cooling, while more smooth anomalies are associated with a less pronounced 660 radiative cooling peak. This effect introduces more variability in min(Q anom ) the stronger the anomalies are. It also explains why retrieved moisture anomalies do not show as extreme min(Q anom ) values as the reference dataset, since the vertical shape of retrieved anomalies is always bound by the smoothing error.
In the real world, much more extreme vertical moisture gradients associated with moisture anomalies can be observed than in the model based reference dataset used here. Albright et al. (2020) discuss an EML scenario over the Northern Atlantic

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Trades with a significant moisture drop that is associated with a minimum cooling rate of about 20 K day −1 . The results of Fig. 10 indicate that while the retrieval is able to broadly distinguish between differently strong moisture anomalies and their associated heating rates, it is unable to properly represent such extreme cooling rate minima due to smoothing. troposphere. We explain this by the dependence of s anom on the absolute humidity, which decreases exponentially with height.

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To make the idea of an EML more graspable and to characterise an EML quantitatively (e.g. by strength, thickness and height), the concept of a moisture anomaly against a loosely fitted but clearly defined reference humidity profile is introduced.
Following the ideas of Johnson et al. (1996) and Stevens et al. (2017) about a coupling of EMLs to the freezing level, EMLs would in this framework constitute a subset of rather strong, vertically confined, lower to mid tropospheric positive moisture anomalies. However, for the scope of this work no clear specification of what distinguishes an EML from other moisture anomalies is attempted, which would require a more dedicated selection and analysis of the test dataset. Instead, the clear aim of this study is a first systematic evaluation of the retrieval's ability to capture moisture anomalies and their characteristics, with particular focus on the more loosely defined EML cases :::: EML ::::::::::: retrievability ::::: based :: on ::::::::::: hyperspectral ::: IR ::::::::::: observations.

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When applying the retrieval to the tropical ocean test dataset, it is found that a large fraction of the absolute retrieval error in humidity can be attributed to smoothing. In particular in the transition region between the boundary layer and the free troposphere, the smoothing error introduces a bias to the retrieved humidity and temperature profiles, which is most likely connected to the sharp humidity drop associated with the stratified barrier between the moist boundary layer and the dry free troposphere in the trade wind region. In the free troposphere, say above 800 hPa, the retrieval shows no significant moisture 710 bias, but a positively skewed error variability, indicating that moist anomalies are typically associated with smaller errors than dry anomalies. This is coherent with the idea that dry anomalies that occur beneath moist anomalies are prone to larger errors due to the reduced sensitivity of the satellite measurement below a moist anomaly.
The analysis of capturing the moisture anomalies' footprint on the heating rate profiles shows that the retrieval is able to capture the general relation between anomaly strength and minimum cooling rate. However, the retrieval shows a particular 725 shortcoming in capturing the most extreme cooling rates associated with strong lower to mid tropospheric anomalies. We attribute this shortcoming to the retrieval's limited ability of resolving strong vertical moisture gradients that are necessary for the most extreme local cooling rates. Vertical moisture gradients in the real world can be a lot stronger than the ones available from the model test dataset (Albright et al., 2020), which means that retrieval errors with respect to peaks in the cooling rates can be large for rather extreme but realistic cases.
Author contributions. MP conducted the radiative transfer and the retrieval calculations and prepared the manuscript. MB and SAB supervised the analysis of the retrieval results, contributed ideas to the manuscript and revised it.